Generally most people stand up to say and to respond to kaddish; why do we do this? Is there anyone with a minhag to sit for either saying or responding to kaddish and the reason behind doing so?
The Kitzur Shulchan Aruch in 15:6 states:
Some say that one need not stand for Kaddish.
However, any Kaddish which catches you standing, like after Hallel, one should [remain] standing until after [responding] Yehei Shmei Rabba.
And some say that one should always stand for Kaddish and other Davar SheBiKedusha, since we should learn a Kal VaChomer from Eglon King of Moab, as it states (Shoftim 3:20) and Ehud came to him, etc. and Ehud said [I have] a word from Gcd for you! and he [the King] stood up.
וַיֹּאמֶר אֵהוּד, דְּבַר-אֱ-לֹקים לִי אֵלֶיךָ; וַיָּקָם, מֵעַל הַכִּסֵּא.
So if Eglon King of Moab - who was an idol worshiper - stood up when being told a word of Gcd, how much more so [should we stand], as member of His nation.
And so one should be stringent.
The Sefardim seem to sit for any Kaddish which catches them sitting, even if they have to stand immediately afterwards. Ashkenazim tend to stand for every Kaddish.